Applying Probability Measures to Abstract Languages

The problem of assigning a probability to each word of a language is considered. Two methods are discussed. One method assigns a probability to a word on the basis of particular measurable features of the language. The second method is applied to languages L(G) generated by a grammar G. A probability is associated with each production of G. These in turn define the word probabilities of each word in the language. The conditions for this assignment to be a probabilistic measure are derived.